Equivalence (REF ) was proved first in [1]} for \(k=1\) , \(1<p<\infty \) , \(W\in A_{p}\)  and \(\varphi \left( x\right) =x^{p}\) . In the case
\(k=1\)  (REF ) was obtained in [2]}, [3]}. Under the conditions \(k=1 \)  and convex \(\varphi \) , (REF ) was obtained in [4]}.
